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<a href="oct_8h.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*</span>
<a name="l00002"></a>00002 <span class="comment"> * Copyright (c) 2010-2011, NVIDIA Corporation</span>
<a name="l00003"></a>00003 <span class="comment"> * All rights reserved.</span>
<a name="l00004"></a>00004 <span class="comment"> *</span>
<a name="l00005"></a>00005 <span class="comment"> * Redistribution and use in source and binary forms, with or without</span>
<a name="l00006"></a>00006 <span class="comment"> * modification, are permitted provided that the following conditions are met:</span>
<a name="l00007"></a>00007 <span class="comment"> *   * Redistributions of source code must retain the above copyright</span>
<a name="l00008"></a>00008 <span class="comment"> *     notice, this list of conditions and the following disclaimer.</span>
<a name="l00009"></a>00009 <span class="comment"> *   * Redistributions in binary form must reproduce the above copyright</span>
<a name="l00010"></a>00010 <span class="comment"> *     notice, this list of conditions and the following disclaimer in the</span>
<a name="l00011"></a>00011 <span class="comment"> *     documentation and/or other materials provided with the distribution.</span>
<a name="l00012"></a>00012 <span class="comment"> *   * Neither the name of NVIDIA Corporation nor the</span>
<a name="l00013"></a>00013 <span class="comment"> *     names of its contributors may be used to endorse or promote products</span>
<a name="l00014"></a>00014 <span class="comment"> *     derived from this software without specific prior written permission.</span>
<a name="l00015"></a>00015 <span class="comment"> *</span>
<a name="l00016"></a>00016 <span class="comment"> * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS &quot;AS IS&quot; AND</span>
<a name="l00017"></a>00017 <span class="comment"> * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED</span>
<a name="l00018"></a>00018 <span class="comment"> * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE</span>
<a name="l00019"></a>00019 <span class="comment"> * DISCLAIMED. IN NO EVENT SHALL &lt;COPYRIGHT HOLDER&gt; BE LIABLE FOR ANY</span>
<a name="l00020"></a>00020 <span class="comment"> * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES</span>
<a name="l00021"></a>00021 <span class="comment"> * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;</span>
<a name="l00022"></a>00022 <span class="comment"> * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND</span>
<a name="l00023"></a>00023 <span class="comment"> * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT</span>
<a name="l00024"></a>00024 <span class="comment"> * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS</span>
<a name="l00025"></a>00025 <span class="comment"> * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</span>
<a name="l00026"></a>00026 <span class="comment"> */</span>
<a name="l00027"></a>00027 
<a name="l00039"></a>00039 <span class="preprocessor">#pragma once</span>
<a name="l00040"></a>00040 <span class="preprocessor"></span>
<a name="l00041"></a>00041 <span class="preprocessor">#include &lt;nih/basic/numbers.h&gt;</span>
<a name="l00042"></a>00042 <span class="preprocessor">#include &lt;<a class="code" href="vector_8h.html" title="Define linear-algebra vector classes.">nih/linalg/vector.h</a>&gt;</span>
<a name="l00043"></a>00043 <span class="preprocessor">#include &lt;nih/linalg/matrix.h&gt;</span>
<a name="l00044"></a>00044 
<a name="l00045"></a>00045 <span class="keyword">namespace </span>nih {
<a name="l00046"></a>00046 
<a name="l00055"></a>00055 
<a name="l00056"></a>00056 
<a name="l00057"></a>00057 
<a name="l00058"></a>00058 
<a name="l00059"></a>00059 NIH_HOST_DEVICE <span class="keywordtype">float</span> <a class="code" href="group__octahedral__functions.html#gae4f57aa8c225e3b15676f3c5cc049d20">oct_basis</a>(<span class="keyword">const</span> int32 i, <span class="keyword">const</span> Vector3f&amp; d);
<a name="l00060"></a>00060 
<a name="l00065"></a>00065 NIH_HOST_DEVICE <span class="keywordtype">float</span> <a class="code" href="group__octahedral__functions.html#ga3875de0131887e4c122d9f76aa6c1ef0" title="evaluate the i-th smooth octahedral basis">oct_smooth_basis</a>(<span class="keyword">const</span> int32 i, <span class="keyword">const</span> Vector3f&amp; omega);
<a name="l00066"></a>00066 
<a name="l00072"></a><a class="code" href="structnih_1_1_oct__basis.html">00072</a> <span class="keyword">struct </span><a class="code" href="structnih_1_1_oct__basis.html">Oct_basis</a>
<a name="l00073"></a>00073 {
<a name="l00074"></a>00074     <span class="keyword">static</span> <span class="keyword">const</span> int32 COEFFS = 8;
<a name="l00075"></a>00075 
<a name="l00080"></a><a class="code" href="structnih_1_1_oct__basis.html#a3416fb501ffa0800555a1d6d155d1ede">00080</a>     NIH_HOST NIH_DEVICE <span class="keyword">static</span> <span class="keywordtype">float</span> <a class="code" href="structnih_1_1_oct__basis.html#a3416fb501ffa0800555a1d6d155d1ede">eval</a>(<span class="keyword">const</span> int32 i, <span class="keyword">const</span> <a class="code" href="structnih_1_1_vector.html">Vector3f</a>&amp; d) { <span class="keywordflow">return</span> <a class="code" href="group__octahedral__functions.html#gae4f57aa8c225e3b15676f3c5cc049d20">oct_basis</a>( i, d ); }
<a name="l00081"></a>00081 
<a name="l00088"></a>00088     <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="structnih_1_1_oct__basis.html#acb3b29cb0c7c734967155a0db1f4cc21">clamped_cosine</a>(<span class="keyword">const</span> <a class="code" href="structnih_1_1_vector.html">Vector3f</a>&amp; normal, <span class="keyword">const</span> <span class="keywordtype">float</span> w, <span class="keywordtype">float</span>* coeffs);
<a name="l00089"></a>00089 
<a name="l00094"></a><a class="code" href="structnih_1_1_oct__basis.html#a65fc8be223ac745b96f1fe8fc6d7b17c">00094</a>     <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="structnih_1_1_oct__basis.html#a65fc8be223ac745b96f1fe8fc6d7b17c">constant</a>(<span class="keywordtype">float</span> k, <span class="keywordtype">float</span>* coeffs)
<a name="l00095"></a>00095     {
<a name="l00096"></a>00096         <span class="keywordflow">for</span> (int32 i = 0; i &lt; 8; ++i)
<a name="l00097"></a>00097             coeffs[i] = k * sqrtf(M_PIf/2.0f);
<a name="l00098"></a>00098     }
<a name="l00099"></a>00099 
<a name="l00102"></a><a class="code" href="structnih_1_1_oct__basis.html#a24c4318d1fff8c5479cb9818d091a762">00102</a>     <span class="keyword">static</span> <span class="keywordtype">float</span> <a class="code" href="structnih_1_1_oct__basis.html#a24c4318d1fff8c5479cb9818d091a762">integral</a>(<span class="keyword">const</span> <span class="keywordtype">float</span>* coeffs)
<a name="l00103"></a>00103     {
<a name="l00104"></a>00104         <span class="keywordtype">float</span> r = 0.0f;
<a name="l00105"></a>00105         <span class="keywordflow">for</span> (int32 i = 0; i &lt; 8; ++i)
<a name="l00106"></a>00106             r += coeffs[i];
<a name="l00107"></a>00107         <span class="keywordflow">return</span> r;
<a name="l00108"></a>00108     }
<a name="l00109"></a>00109 
<a name="l00112"></a>00112     <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Vector_type&gt;
<a name="l00113"></a><a class="code" href="structnih_1_1_oct__basis.html#acb720797ed36adc43ee4c40d8189ade6">00113</a>     <span class="keyword">static</span> <span class="keywordtype">float</span> <a class="code" href="structnih_1_1_oct__basis.html#a24c4318d1fff8c5479cb9818d091a762">integral</a>(<span class="keyword">const</span> Vector_type&amp; coeffs)
<a name="l00114"></a>00114     {
<a name="l00115"></a>00115         <span class="keywordtype">float</span> r = 0.0f;
<a name="l00116"></a>00116         <span class="keywordflow">for</span> (int32 i = 0; i &lt; 8; ++i)
<a name="l00117"></a>00117             r += coeffs[i];
<a name="l00118"></a>00118         <span class="keywordflow">return</span> r;
<a name="l00119"></a>00119     }
<a name="l00120"></a>00120 
<a name="l00124"></a><a class="code" href="structnih_1_1_oct__basis.html#a0278f1597434a516d596659ec9501d89">00124</a>     <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="structnih_1_1_oct__basis.html#a0278f1597434a516d596659ec9501d89">solve</a>(<span class="keywordtype">float</span>* coeffs) {}
<a name="l00125"></a>00125 };
<a name="l00126"></a>00126 
<a name="l00128"></a>00128 NIH_HOST_DEVICE <span class="keywordtype">float</span> <a class="code" href="group__octahedral__functions.html#ga3875de0131887e4c122d9f76aa6c1ef0" title="evaluate the i-th smooth octahedral basis">oct_smooth_basis</a>(<span class="keyword">const</span> int32 i, <span class="keyword">const</span> Vector3f&amp; omega);
<a name="l00129"></a>00129 
<a name="l00135"></a><a class="code" href="structnih_1_1_oct__smooth__basis.html">00135</a> <span class="keyword">struct </span><a class="code" href="structnih_1_1_oct__smooth__basis.html">Oct_smooth_basis</a>
<a name="l00136"></a>00136 {
<a name="l00137"></a>00137     <span class="keyword">static</span> <span class="keyword">const</span> int32 COEFFS = 8;
<a name="l00138"></a>00138 
<a name="l00143"></a><a class="code" href="structnih_1_1_oct__smooth__basis.html#aa14a75a18d247804bad176c609a7a0e8">00143</a>     NIH_HOST_DEVICE <span class="keyword">static</span> <span class="keywordtype">float</span> <a class="code" href="structnih_1_1_oct__smooth__basis.html#aa14a75a18d247804bad176c609a7a0e8">eval</a>(<span class="keyword">const</span> int32 i, <span class="keyword">const</span> <a class="code" href="structnih_1_1_vector.html">Vector3f</a>&amp; d) { <span class="keywordflow">return</span> <a class="code" href="group__octahedral__functions.html#ga3875de0131887e4c122d9f76aa6c1ef0" title="evaluate the i-th smooth octahedral basis">oct_smooth_basis</a>( i, d ); }
<a name="l00144"></a>00144 
<a name="l00151"></a>00151     <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="structnih_1_1_oct__smooth__basis.html#aa0169c6efd1730c823590835cd10418a">clamped_cosine</a>(<span class="keyword">const</span> <a class="code" href="structnih_1_1_vector.html">Vector3f</a>&amp; normal, <span class="keyword">const</span> <span class="keywordtype">float</span> w, <span class="keywordtype">float</span>* coeffs);
<a name="l00152"></a>00152 
<a name="l00157"></a><a class="code" href="structnih_1_1_oct__smooth__basis.html#a8cc76fb6689cc5cddd5923badce7b65a">00157</a>     <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="structnih_1_1_oct__smooth__basis.html#a8cc76fb6689cc5cddd5923badce7b65a">constant</a>(<span class="keywordtype">float</span> k, <span class="keywordtype">float</span>* coeffs)
<a name="l00158"></a>00158     {
<a name="l00159"></a>00159         <span class="keywordflow">for</span> (int32 i = 0; i &lt; 8; ++i)
<a name="l00160"></a>00160             coeffs[i] = k * s_K[i];
<a name="l00161"></a>00161     }
<a name="l00162"></a>00162 
<a name="l00165"></a><a class="code" href="structnih_1_1_oct__smooth__basis.html#ac44cf16365644cc8ee5e92347e4b3070">00165</a>     <span class="keyword">static</span> <span class="keywordtype">float</span> <a class="code" href="structnih_1_1_oct__smooth__basis.html#ac44cf16365644cc8ee5e92347e4b3070">integral</a>(<span class="keyword">const</span> <span class="keywordtype">float</span>* coeffs)
<a name="l00166"></a>00166     {
<a name="l00167"></a>00167         <span class="keywordtype">float</span> r = 0.0f;
<a name="l00168"></a>00168         <span class="keywordflow">for</span> (int32 i = 0; i &lt; 8; ++i)
<a name="l00169"></a>00169             r += coeffs[i];
<a name="l00170"></a>00170         <span class="keywordflow">return</span> r;
<a name="l00171"></a>00171     }
<a name="l00172"></a>00172 
<a name="l00175"></a>00175     <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Vector_type&gt;
<a name="l00176"></a><a class="code" href="structnih_1_1_oct__smooth__basis.html#a76b5bd9b8b77e8f6bdaa3e6eb987b080">00176</a>     <span class="keyword">static</span> <span class="keywordtype">float</span> <a class="code" href="structnih_1_1_oct__smooth__basis.html#ac44cf16365644cc8ee5e92347e4b3070">integral</a>(<span class="keyword">const</span> Vector_type&amp; coeffs)
<a name="l00177"></a>00177     {
<a name="l00178"></a>00178         <span class="keywordtype">float</span> r = 0.0f;
<a name="l00179"></a>00179         <span class="keywordflow">for</span> (int32 i = 0; i &lt; 8; ++i)
<a name="l00180"></a>00180             r += coeffs[i];
<a name="l00181"></a>00181         <span class="keywordflow">return</span> r;
<a name="l00182"></a>00182     }
<a name="l00183"></a>00183 
<a name="l00188"></a><a class="code" href="structnih_1_1_oct__smooth__basis.html#a68628b961af6d2c665fe1db6615fb027">00188</a>     <span class="keyword">static</span> <span class="keywordtype">float</span> <a class="code" href="structnih_1_1_oct__smooth__basis.html#a68628b961af6d2c665fe1db6615fb027">G</a>(<span class="keyword">const</span> int32 i, <span class="keyword">const</span> int32 j) { <span class="keywordflow">return</span> s_G[i][j]; }
<a name="l00189"></a>00189 
<a name="l00193"></a>00193     <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="structnih_1_1_oct__smooth__basis.html#a4cf03f31e968129821a58231166ae3b6">solve</a>(<span class="keywordtype">float</span>* coeffs);
<a name="l00194"></a>00194 
<a name="l00195"></a>00195 <span class="keyword">private</span>:
<a name="l00196"></a>00196     <span class="keyword">struct </span>Initializer { Initializer(); };
<a name="l00197"></a>00197 
<a name="l00198"></a>00198     <span class="keyword">friend</span> Initializer;
<a name="l00199"></a>00199 
<a name="l00200"></a>00200     <span class="keyword">static</span> Matrix&lt;float,8,8&gt; s_G;
<a name="l00201"></a>00201     <span class="keyword">static</span> <span class="keywordtype">float</span>             s_K[8];
<a name="l00202"></a>00202     <span class="keyword">static</span> Initializer       s_I;
<a name="l00203"></a>00203 };
<a name="l00204"></a>00204 
<a name="l00205"></a>00205 <span class="keyword">static</span> Vector3f s_oct_verts[6] = {
<a name="l00206"></a>00206     Vector3f(+1, 0, 0),
<a name="l00207"></a>00207     Vector3f(-1, 0, 0),
<a name="l00208"></a>00208     Vector3f( 0,+1, 0),
<a name="l00209"></a>00209     Vector3f( 0,-1, 0),
<a name="l00210"></a>00210     Vector3f( 0, 0,+1),
<a name="l00211"></a>00211     Vector3f( 0, 0,-1),
<a name="l00212"></a>00212 };
<a name="l00213"></a>00213 <span class="keyword">static</span> int32 s_oct_faces[8][3] = {
<a name="l00214"></a>00214     {0,2,4},
<a name="l00215"></a>00215     {2,1,4},
<a name="l00216"></a>00216     {1,3,4},
<a name="l00217"></a>00217     {3,0,4},
<a name="l00218"></a>00218     {2,0,5},
<a name="l00219"></a>00219     {1,2,5},
<a name="l00220"></a>00220     {3,1,5},
<a name="l00221"></a>00221     {0,3,5},
<a name="l00222"></a>00222 };
<a name="l00223"></a>00223 
<a name="l00224"></a>00224 <span class="comment">// evaluate the i-th octahedral basis</span>
<a name="l00225"></a><a class="code" href="group__octahedral__functions.html#gae4f57aa8c225e3b15676f3c5cc049d20">00225</a> <span class="keyword">inline</span> NIH_HOST NIH_DEVICE <span class="keywordtype">float</span> <a class="code" href="group__octahedral__functions.html#gae4f57aa8c225e3b15676f3c5cc049d20">oct_basis</a>(<span class="keyword">const</span> int32 i, <span class="keyword">const</span> <a class="code" href="structnih_1_1_vector.html">Vector3f</a>&amp; omega)
<a name="l00226"></a>00226 {
<a name="l00227"></a>00227     <span class="keyword">const</span> <span class="keywordtype">float</span> <a class="code" href="group__vectors.html#gaef3221bb95a71d1743f7df1673082cbf">norm</a> = sqrtf(2.0f/M_PIf); <span class="comment">// sqrt(8) / sqrt(4*PI)</span>
<a name="l00228"></a>00228 
<a name="l00229"></a>00229     <span class="comment">// oct_basis</span>
<a name="l00230"></a>00230     <span class="keywordflow">return</span>
<a name="l00231"></a>00231         ((1 - 2*(((i+1)&gt;&gt;1)&amp;1))*omega[0] &gt; 0.0f ? 1.0f : 0.0f)*
<a name="l00232"></a>00232         ((1 - 2*((i&gt;&gt;1)&amp;1)    )*omega[1] &gt; 0.0f ? 1.0f : 0.0f)*
<a name="l00233"></a>00233         ((1 - 2*(i&gt;&gt;2)        )*omega[2] &gt; 0.0f ? 1.0f : 0.0f) * norm;
<a name="l00234"></a>00234 <span class="comment">/*</span>
<a name="l00235"></a>00235 <span class="comment">    // the i-th basis is defined by all directions inside the spherical triangle {v1,v2,v3}</span>
<a name="l00236"></a>00236 <span class="comment">    const Vector3f v1 = s_oct_verts[ s_oct_faces[i][0] ];</span>
<a name="l00237"></a>00237 <span class="comment">    const Vector3f v2 = s_oct_verts[ s_oct_faces[i][1] ];</span>
<a name="l00238"></a>00238 <span class="comment">    const Vector3f v3 = s_oct_verts[ s_oct_faces[i][2] ];</span>
<a name="l00239"></a>00239 <span class="comment"></span>
<a name="l00240"></a>00240 <span class="comment">    //</span>
<a name="l00241"></a>00241 <span class="comment">    // check whether omega intersects {v1,v2,v3}</span>
<a name="l00242"></a>00242 <span class="comment">    //</span>
<a name="l00243"></a>00243 <span class="comment"></span>
<a name="l00244"></a>00244 <span class="comment">    // equivalent to checking that all three dot products with omega are positive, but we can make it cheaper...</span>
<a name="l00245"></a>00245 <span class="comment"></span>
<a name="l00246"></a>00246 <span class="comment">    // first, assume v3 is the north/south pole, and check whether omega.z is on the same side or not.</span>
<a name="l00247"></a>00247 <span class="comment">    if (v3[2] * omega[2] &lt; 0.0f)</span>
<a name="l00248"></a>00248 <span class="comment">        return 0.0f;</span>
<a name="l00249"></a>00249 <span class="comment"></span>
<a name="l00250"></a>00250 <span class="comment">    // second, project omega on the XY plane, and test whether it intersects the edge (v1,v2):</span>
<a name="l00251"></a>00251 <span class="comment">    // in order for this to happen, both dot products of omega with v1 and v2 have to be positive.</span>
<a name="l00252"></a>00252 <span class="comment">    if (dot(v1,omega) &lt; 0.0f || dot(v2,omega) &lt; 0.0f)</span>
<a name="l00253"></a>00253 <span class="comment">        return 0.0f;</span>
<a name="l00254"></a>00254 <span class="comment"></span>
<a name="l00255"></a>00255 <span class="comment">    return norm;</span>
<a name="l00256"></a>00256 <span class="comment">    */</span>
<a name="l00257"></a>00257 }
<a name="l00258"></a>00258 
<a name="l00259"></a>00259 <span class="comment">// evaluate the i-th smooth octahedral basis</span>
<a name="l00260"></a><a class="code" href="group__octahedral__functions.html#ga3875de0131887e4c122d9f76aa6c1ef0">00260</a> <span class="keyword">inline</span> NIH_HOST_DEVICE <span class="keywordtype">float</span> <a class="code" href="group__octahedral__functions.html#ga3875de0131887e4c122d9f76aa6c1ef0" title="evaluate the i-th smooth octahedral basis">oct_smooth_basis</a>(<span class="keyword">const</span> int32 i, <span class="keyword">const</span> <a class="code" href="structnih_1_1_vector.html">Vector3f</a>&amp; omega)
<a name="l00261"></a>00261 {
<a name="l00262"></a>00262     <span class="keyword">const</span> <a class="code" href="structnih_1_1_vector.html">Vector3f</a> c(
<a name="l00263"></a>00263         -0.66666666666666666666f * (((i+1)&gt;&gt;1) &amp; 1) + 0.33333333333333333333f,
<a name="l00264"></a>00264         -0.66666666666666666666f * ((i&gt;&gt;1)     &amp; 1) + 0.33333333333333333333f,
<a name="l00265"></a>00265         -0.66666666666666666666f * (i&gt;&gt;2)           + 0.33333333333333333333f );
<a name="l00266"></a>00266 
<a name="l00267"></a>00267     <span class="keyword">const</span> <span class="keywordtype">float</span> N    = 2.0f;
<a name="l00268"></a>00268     <span class="keyword">const</span> <span class="keywordtype">float</span> <a class="code" href="group__vectors.html#gaef3221bb95a71d1743f7df1673082cbf">norm</a> = 2.170803763674771f; <span class="comment">//sqrtf( (N + 1) / (2.0f * M_PIf) );</span>
<a name="l00269"></a>00269 
<a name="l00270"></a>00270     <span class="keyword">const</span> <span class="keywordtype">float</span> d = <a class="code" href="group__vectors.html#gab2b34b1991185fc29890973777b60e54">max</a>( <a class="code" href="group__vectors.html#ga299bb7e770db20680a383864db4bd843">dot</a>( omega, c ), 0.0f );
<a name="l00271"></a>00271     <span class="keywordflow">return</span> fast_pow( d, N ) * <a class="code" href="group__vectors.html#gaef3221bb95a71d1743f7df1673082cbf">norm</a>;
<a name="l00272"></a>00272 }
<a name="l00273"></a>00273 
<a name="l00277"></a>00277 } <span class="comment">// namespace nih</span>
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